What kinds of finger foods can I give my 5-month-old?
Five months is actually still quite early to be considering finger (or table) foods, as they aren't typically recommended until babies are at least 7 to 9 months. In some cases, table foods may be introduced even later, depending on each individual baby's skill level. By skill level, I not only mean safely and successfully chewing (or gumming), getting food to the back of one's mouth and then swallowing, but also the ability to pick up finger foods and get them to one's mouth. Babies start to be able to use their thumb and first finger to successfully pick up objects (including food) closer to the end of the first year, conveniently around the same time that they are better able to safely eat and swallow more table foods and textures.
In light of the clear recommendation to avoid giving 5-month-olds any sort of finger foods, let me instead point out that this is the perfect time to consider what baby foods to introduce your baby to. The current recommendation for starting solid foods is to start some time between 4 to 6 months, when your baby shows signs of solid-food readiness. Both baby cereals and pureed meats are particularly important as a baby's primary source of iron, and can now both be introduced right from the start and then continued throughout the first year, along with fruits and vegetables. For a much more detailed explanation and approach to getting your baby off to a healthy nutritional start, feel free to check out the "Baby Bites: Starting Solid Foods" chapter in the 2nd Edition of Food Fights.